Confine contour lines to region defined by data

I am using contour() to construct contour lines onto a 2D grid of data defined by the first two columns of "tog.txt," with the value defined by the third column. This data can have 10^3 or more rows. I would like to confine these lines to exist only in the region where the data exists.

I plot the scatter data as well as the border that bounds the data with boundary() for visualization.

The results of each attempt are attached. How can I ensure the contour lines are terminated by the data boundary?

togtxt = load('tog.txt');

x1 = togtxt(:,1);
y1 = togtxt(:,2);
c1 = togtxt(:,3);

% ---- customize figure -------------------------------------------------------

f(1)=figure;
hold all
ax = gca;

set(gca,'LineWidth',1.3,'TickLength',[0.015 0.015],'plotboxaspectratio',[1 1 1]); % size of ticks
set(gca,'ColorScale','log')
xscale log

jjj = boundary(x1,y1);
plot(x1(jjj),y1(jjj));

scatter(togtxt(:,1),togtxt(:,2),2,'filled');

N = 120;

%%% attempt 1

v1 = logspace(log10(min(c1)),log10(max(c1)),50);
I = scatteredInterpolant(x1,y1,c1);
X = linspace(min(x1),max(x1),N);
Y = linspace(min(y1),max(y1),N);
[X,Y] = meshgrid(X,Y);
Z = I(X,Y);
contour(X,Y,Z,v1);
colorbar


%%% attempt 2
% v1 = logspace(log10(min(c1)),log10(max(c1)),50);
% xv = linspace(min(x1),max(x1),N); 
% yv = linspace(min(y1),max(y1),N); % will run out of memory unless N small
% [Xm,Ym] = ndgrid(xv,yv);
% MFm = griddata(x1,y1,c1,Xm,Ym);
% contour(Xm, Ym, MFm,v1)

Answer 1

[Mathieu NOE]

hello

sorry for not putting alot of comments, but I am in a hurry....

here 's my first suggestion, maybe a little dirty but it works so far

togtxt = load('tog.txt');
x1 = togtxt(:,1);
y1 = togtxt(:,2);
c1 = togtxt(:,3);
% ---- customize figure -------------------------------------------------------
f(1)=figure;
hold all
ax = gca;
set(gca,'LineWidth',1.3,'TickLength',[0.015 0.015],'plotboxaspectratio',[1 1 1]); % size of ticks
set(gca,'ColorScale','log')
jjj = boundary(x1,y1,0.5);

% boundary points 
x1b = x1(jjj);
y1b = y1(jjj);
c1b = c1(jjj);

plot(x1b,y1b,'b','linewidth',3);
scatter(x1,y1,2,c1,'filled');
N = 15;

v1 = logspace(log10(min(c1)),log10(max(c1)),N);
I = scatteredInterpolant(x1,y1,c1);
X = linspace(min(x1),max(x1),100);
Y = linspace(min(y1),max(y1),100);
[X,Y] = meshgrid(X,Y);
Z = I(X,Y);

[C,h] = contour(X,Y,Z,v1,'edgecolor','none'); % do not plot yet so use 'edgecolor','none'
[m,n] = size(C);

% do a bit of post processing to avoid contour lines go out of boundary 
[matchingValues, ind, ~] = intersect(C(1,:), v1);
ind = [ind; n+1]; % add end (+1) 
for k = 1:numel(ind)-1
    xc = C(1,ind(k)+1:ind(k+1)-1);
    yc = C(2,ind(k)+1:ind(k+1)-1);
    % use inpolygon to remove data outside boundary
    in = inpolygon(xc,yc,x1b,y1b);
    xc = xc(in);
    yc = yc(in);
    plot(xc,yc,'k');
end
hold off
xscale log

[Mathieu NOE]

Some improvements wih now colored contour lines ....if you prefer

togtxt = load('tog.txt');
x1 = togtxt(:,1);
y1 = togtxt(:,2);
c1 = togtxt(:,3);
% ---- customize figure -------------------------------------------------------
f(1)=figure;
hold all
ax = gca;
set(gca,'LineWidth',1.3,'TickLength',[0.015 0.015],'plotboxaspectratio',[1 1 1]); % size of ticks
set(gca,'ColorScale','log')
jjj = boundary(x1,y1,0.5);

% boundary points 
x1b = x1(jjj);
y1b = y1(jjj);
c1b = c1(jjj);

plot(x1b,y1b,'b','linewidth',3);
scatter(x1,y1,2,c1,'filled');
N = 15;

v1 = logspace(log10(min(c1)),log10(max(c1)),N);
I = scatteredInterpolant(x1,y1,c1);
X = linspace(min(x1),max(x1),100);
Y = linspace(min(y1),max(y1),100);
[X,Y] = meshgrid(X,Y);
Z = I(X,Y);

[C,h] = contour(X,Y,Z,v1,'edgecolor','none'); % do not plot yet so use 'edgecolor','none'
[m,n] = size(C);

% do a bit of post processing to avoid contour lines go out of boundary 
[matchingValues, ind, ~] = intersect(C(1,:), v1);
ind = [ind; n+1]; % add end (+1) 
for k = 1:numel(ind)-1
    xc = C(1,ind(k)+1:ind(k+1)-1);
    yc = C(2,ind(k)+1:ind(k+1)-1);
    % use inpolygon to remove data outside boundary
    in = inpolygon(xc,yc,x1b,y1b);
    xc = xc(in);
    yc = yc(in);
    
    %plot(xc,yc,'k'); % black contour lines
    
    % colored contour lines
    cc = interp2(X,Y,Z,xc,yc);
    patch([xc NaN],[yc NaN],[cc 0],'edgecolor','interp','linewidth',2)
end
hold off
xscale log

●

Warning: Error creating or updating Patch
Error in value of property FaceVertexCData
Number of colors must equal number of vertices.

[Mathieu NOE]

maybe someone will find the trick to avoid the warning message with the patch solution above

otherwise you can also work with the regular plot function, but here again there is a little bit of extra work to do if you really need the log scaled color display

for simplicity I did it for a linear scale color rendering - if that works for you

of course as the contour and scatter plot use the same colors , they are barelly distinguisable - you can modify the color options (at least it proves the contour lines use the correct colors ! )

togtxt = load('tog.txt');
x1 = togtxt(:,1);
y1 = togtxt(:,2);
c1 = togtxt(:,3);
% ---- customize figure -------------------------------------------------------
f(1)=figure;

set(gca,'LineWidth',1.3,'TickLength',[0.015 0.015],'plotboxaspectratio',[1 1 1]); % size of ticks
% set(gca,'ColorScale','log')

map = colormap(); % 

hold all
ax = gca;

jjj = boundary(x1,y1,0.5);

% boundary points 
x1b = x1(jjj);
y1b = y1(jjj);
c1b = c1(jjj);

plot(x1b,y1b,'b','linewidth',3);
scatter(x1,y1,2,c1,'filled');

N = 20; % number of contour lines 

v1 = logspace(log10(min(c1)),log10(max(c1)),N);
I = scatteredInterpolant(x1,y1,c1);
X = linspace(min(x1),max(x1),100);
Y = linspace(min(y1),max(y1),100);
[X,Y] = meshgrid(X,Y);
Z = I(X,Y);

[C,h] = contour(X,Y,Z,v1,'edgecolor','none'); % do not plot yet so use 'edgecolor','none'
[m,n] = size(C);

% do a bit of post processing to avoid contour lines go out of boundary 
[matchingValues, ind, ~] = intersect(C(1,:), v1);
ind = [ind; n+1]; % add end (+1) 
for k = 1:numel(ind)-1
    xc = C(1,ind(k)+1:ind(k+1)-1);
    yc = C(2,ind(k)+1:ind(k+1)-1);
    % use inpolygon to remove data outside boundary
    in = inpolygon(xc,yc,x1b,y1b);
    xc = xc(in);
    yc = yc(in);
    
    % colored contour lines
    cc = interp2(X,Y,Z,xc,yc);
    pp = plot(xc,yc); % capture the line handle when you plot it
    row_index = 1+floor((size(map,1)-1)*(mean(cc) - min(c1b))/ (max(c1b) - min(c1b)));
    cd = map(row_index,:);
    set(pp,'Color',cd)
    
end
hold off
xscale log

[Zachary]

Thanks @Mathieu NOE for your help. I will try these out just as soon as I have a moment.

Zachary

[Mathieu NOE]

my pleasure !

[Zachary]

It's working well, @Mathieu NOE. Thanks.

Since we use patch(), are we now unable to provide contour labels in the usual way using something like

clabel(C2,h,[10 100],'FontSize',14,'Color','w'); % ?

It seems not to work when I try it.

[Mathieu NOE]

this is a workaround :

togtxt = load('tog.txt');
x1 = togtxt(:,1);
y1 = togtxt(:,2);
c1 = togtxt(:,3);
% ---- customize figure -------------------------------------------------------
f(1)=figure;
hold all
ax = gca;
set(gca,'LineWidth',1.3,'TickLength',[0.015 0.015],'plotboxaspectratio',[1 1 1]); % size of ticks
set(gca,'ColorScale','log')
jjj = boundary(x1,y1,0.5);

% boundary points 
x1b = x1(jjj);
y1b = y1(jjj);
c1b = c1(jjj);

plot(x1b,y1b,'b','linewidth',3);
scatter(x1,y1,2,c1,'filled');
N = 10;

v1 = logspace(log10(min(c1)),log10(max(c1)),N);
I = scatteredInterpolant(x1,y1,c1);
X = linspace(min(x1),max(x1),100);
Y = linspace(min(y1),max(y1),100);
[X,Y] = meshgrid(X,Y);
Z = I(X,Y);

[C,h] = contour(X,Y,Z,v1,'edgecolor','none'); % do not plot yet so use 'edgecolor','none'
[m,n] = size(C);

% do a bit of post processing to avoid contour lines go out of boundary 
[matchingValues, ind, ~] = intersect(C(1,:), v1);
ind = [ind; n+1]; % add end (+1) 

for k = 1:numel(ind)-1
    xc = C(1,ind(k)+1:ind(k+1)-1);
    yc = C(2,ind(k)+1:ind(k+1)-1);
    % use inpolygon to remove data outside boundary
    in = inpolygon(xc,yc,x1b,y1b);
    xc = xc(in);
    yc = yc(in);
    
    % colored contour lines
    cc = interp2(X,Y,Z,xc,yc);
    patch([xc NaN],[yc NaN],[cc 0],'edgecolor','interp','linewidth',2)
    % add some contour values alike clabel 
    indx=floor(numel(xc)/2);
    tt = text(xc(indx),yc(indx),num2str(mean(cc),3));
    %% orient text along the curve 
    % Data aspect ratio
    da = daspect();
    ard = da(2) / da(1);
    % Plot (box) aspect ratio
    pa = pbaspect();
    arp = pa(2) / pa(1);
    angl = 180/pi*atan2(gradient(yc)/ard*arp,gradient(xc));
    set(tt,'Rotation',angl(indx));
    
end

hold off
xscale log

●

Warning: Error creating or updating Patch
Error in value of property FaceVertexCData
Number of colors must equal number of vertices.

[Zachary]

Thank you @Mathieu NOE !

[Mathieu NOE]

again, my pleasure !

have a great day